universary milestone in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reduction / cpx_lleq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lleq.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lleq.ma
index 4b0257e6f453b6bf707fa8271278761e63482bab..8eb198df41519cc24a4f28924f5460c6399ef5ad 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lleq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lleq.ma
@@ -12,18 +12,20 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/relocation/lleq_lleq.ma".
-include "basic_2/reduction/cpx.ma".
+include "basic_2/multiple/lleq_drop.ma".
+include "basic_2/reduction/cpx_llpx_sn.ma".
 
 (* CONTEXT-SENSITIVE EXTENDED PARALLEL REDUCTION FOR TERMS ******************)
 
 (* Properties on lazy equivalence for local environments ********************)
 
-lemma lleq_cpx_trans: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡[h, g] T2 →
-                      ∀L1. L1 ⋕[0, T1] L2 → ⦃G, L1⦄ ⊢ T1 ➡[h, g] T2.
-#h #g #G #L2 #T1 #T2 #H elim H -G -L2 -T1 -T2 /2 width=2 by cpx_sort/
-[ #I #G #L2 #K2 #V1 #V2 #W2 #i #HLK2 #_ #HVW2 #IHV12 #L1 #H elim (lleq_inv_lref_ge_dx … H … HLK2) -L2
-  /3 width=7 by cpx_delta/
+lemma lleq_cpx_trans: ∀h,o,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡[h, o] T2 →
+                      ∀L1. L1 ≡[T1, 0] L2 → ⦃G, L1⦄ ⊢ T1 ➡[h, o] T2.
+#h #o #G #L2 #T1 #T2 #H elim H -G -L2 -T1 -T2 /2 width=2 by cpx_st/
+[ #I #G #L2 #K2 #V1 #V2 #W2 #i #HLK2 #_ #HVW2 #IHV12 #L1 #H elim (lleq_fwd_lref_dx … H … HLK2) -L2
+  [ #H elim (ylt_yle_false … H) //
+  | * /3 width=7 by cpx_delta/
+  ]
 | #a #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #H elim (lleq_inv_bind_O … H) -H
   /3 width=1 by cpx_bind/
 | #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #H elim (lleq_inv_flat … H) -H
@@ -31,12 +33,23 @@ lemma lleq_cpx_trans: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡[h, g] T2 →
 | #G #L2 #V2 #T1 #T #T2 #_ #HT2 #IHT1 #L1 #H elim (lleq_inv_bind_O … H) -H
   /3 width=3 by cpx_zeta/
 | #G #L2 #W1 #T1 #T2 #_ #IHT12 #L1 #H elim (lleq_inv_flat … H) -H
-  /3 width=1 by cpx_tau/
+  /3 width=1 by cpx_eps/
 | #G #L2 #W1 #W2 #T1 #_ #IHW12 #L1 #H elim (lleq_inv_flat … H) -H
-  /3 width=1 by cpx_ti/
+  /3 width=1 by cpx_ct/
 | #a #G #L1 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L1 #H elim (lleq_inv_flat … H) -H
   #HV1 #H elim (lleq_inv_bind_O … H) -H /3 width=1 by cpx_beta/
 | #a #G #L1 #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV1 #IHW12 #IHT12 #L1 #H elim (lleq_inv_flat … H) -H
   #HV1 #H elim (lleq_inv_bind_O … H) -H /3 width=3 by cpx_theta/
 ]
 qed-.
+
+lemma cpx_lleq_conf: ∀h,o,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡[h, o] T2 →
+                     ∀L1. L2 ≡[T1, 0] L1 → ⦃G, L1⦄ ⊢ T1 ➡[h, o] T2.
+/3 width=3 by lleq_cpx_trans, lleq_sym/ qed-.
+
+lemma cpx_lleq_conf_sn: ∀h,o,G. c_r_confluent1 … (cpx h o G) (lleq 0).
+/3 width=6 by cpx_llpx_sn_conf, lift_mono, ex2_intro/ qed-.
+
+lemma cpx_lleq_conf_dx: ∀h,o,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡[h, o] T2 →
+                        ∀L1. L1 ≡[T1, 0] L2 → L1 ≡[T2, 0] L2.
+/4 width=6 by cpx_lleq_conf_sn, lleq_sym/ qed-.